the annual household cost of telephone service in the US increased at a relatively constant rate of $27.80 per year from 1981 to 2001. IN 2001 the annual household cost of telephone service was $914.
a:What was the annual household cost of telephone service in 1981?
B: Write an equation that gives the annual household cost of telephone service as a function of the number of year since 1981.
C: find the household cost of telephone service in 2000
a: To find the annual household cost of telephone service in 1981, we can use the given information that the cost increased at a relatively constant rate of $27.80 per year from 1981 to 2001. Since the increase is constant, we can subtract $27.80 for each year from 2001 to 1981.
Calculating the number of years from 2001 to 1981, we get: 2001 - 1981 = 20 years.
Now, multiply $27.80 by the number of years: $27.80 * 20 = $556.
Therefore, the annual household cost of telephone service in 1981 was $556.
b: To write an equation that gives the annual household cost of telephone service as a function of the number of years since 1981, we can use the information that the cost increases at a constant rate of $27.80 per year.
Let's denote the annual household cost of telephone service as C and the number of years since 1981 as t. Since the cost increases at a constant rate, we can write the equation as:
C = 27.80t + C0
where C0 represents the initial cost in 1981.
c: To find the household cost of telephone service in 2000, we can use the same equation from part b and substitute the number of years, t, with 2000 - 1981 = 19 years.
Using the equation C = 27.80t + C0, we substitute t with 19 and rearrange the equation:
C = 27.80 * 19 + C0
Now, we also know that in 2001 the annual household cost of telephone service was $914. Substituting C with 914, we have:
914 = 27.80 * 19 + C0
Now we can solve for C0:
914 - 27.80 * 19 = C0
Calculating the result, we find:
914 - 528.20 = C0
385.80 = C0
Therefore, the household cost of telephone service in 2000 was $385.80.